Assignment: Public Goods and Public Choices

1. Alfie, Bill, and Coco each value police protection differently. Alfie's demand for public goods is Q = 40-5P. Bill's demand is Q = 80-12P, and Coco's and demand is Q =100-10P. If the marginal cost of providing for police protection is $12, what is the socially optimal level police protection? Under Lindahl pricing, what share of the tax burden would each of the three people pay?

2. There are three groups in a community. Their demand for the television in hours of programming, T, are given respectively by

MB₁ = $100 - .5T
MB₂ = $200 -.5T
MB₃= $200 - T

Supposed public television is a pure public good that can be produced at a constant marginal cost of $300 per hour.

a. What is the efficient number of hours of public television?
b. What are the optimal tax prices in this situation?

3. Listed below are the net benefits (measured in billions of dollars) that will result from the passage of two legislative bills X and Y.

a. Identify the logrolling opportunity present in this situation.
b. What are the potential gains to the voters?
c. Explain how logrolling can increase social efficiency.

4. Three individuals consume a good and their demand functions are expressed as

P₁ =1.5 - 0.005Q
P₂ = 4.5 - 0.007Q
P₃ = 3.0 - 0.002Q

Where P represents price in dollars per unit and Q represents output in units per day. The marginal cost of providing this service s given as a constant $5.00 per unit. Determine the efficient level of output of this public good. What are the Lindahl tax prices?

5. The city of MT has 100 residents who have identical demand functions for park area: P =l000-9.95Q. The marginal cost of maintaining lake area is MC (Q) =1500 + 5Q. Lake area is a public good. That is, if the city of MT provides public access lake area, all the residents can enjoy the area. If the city of MT does not offer public lake area, how much area of lake area will each individual residents maintain on their own? What is the optimal area of public lakes in MT? What flat tax should MT implement on residents for units of lake area the city provides? With this flat tax, what is the total contribution of each resident for the lake?

6. The most popular State Park in Tennessee recently reached the point where a common property resource problem (congestion) arose-too many people hunted for wild turkeys each season. The turkey population became over hunted, and was in peril. An economist at the local university studied the problem for the managers of the park and estimated the following cost and benefit relationships.

Demand: P =10 - 0.008Q
Marginal Social Cost: MSC =1.00 + 0.0067Q
Marginal Private Cost: MPC =1.00 + 0.0010Q

The variable Q represents the number of turkeys killed each season, and price P is in hundreds ($).

a. Determine the equilibrium number of turkeys killed per season, when there is an unlimited access to the park.
b. Determined the per-turkey fee that must be charged to reduce the harvest to the efficient level.
c. Determined the social loss of unlimited hunting of the turkeys.

7. Explain what is meant by political equilibrium and how political equilibrium relates to Lindahl equilibrium. Illustrate your explanation with a diagram.

8. Suppose that the residents of a small community are voting for a Fourth of July fireworks display. The marginal benefits of the display durations (where the duration of the display increases from 1 to 4) are shown in the table below.

If each voter is assigned a tax share of $50, what is the political equilibrium under majority rule? Show that this equilibrium does not result in the efficient output of fireworks. Show how the Lindahl equilibrium will different from the political equilibrium under majority rule.